Skip to main content
Log in

Construction of maximal unramified p-extensions with prescribed Galois groups

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Ferrero, B., Washington, L.C.: The Iwasawa invariant μ p vanishes for abelian number fields. Ann. Math. 109, 377–395 (1979)

    Article  MathSciNet  Google Scholar 

  2. Fontaine, J.-M., Mazur, B.: Geometric Galois representations. In: Elliptic Curves, Modular Forms, & Fermat’s Last Theorem (Hong Kong, 1993). Ser. Number Theory, vol. I, pp. 41–78. International Press, Cambridge (1995),

    Google Scholar 

  3. Fröhlich, A.: Central Extensions, Galois Groups, and Ideal Class Groups of Number Fields. Contemporary Mathematics, vol. 24. American Mathematical Society, Providence (1983)

    MATH  Google Scholar 

  4. Horie, K.: A note on basic Iwasawa λ-invariants of imaginary quadratic fields. Invent. Math. 88, 31–38 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  5. Iwasawa, K.: A note on class numbers of algebraic number fields. Abh. Math. Semin. Univ. Hamb. 20, 257–258 (1956)

    MathSciNet  MATH  Google Scholar 

  6. Iwasawa, K.: A note on the group of units of an algebraic number field. J. Math. Pure Appl. 35, 189–192 (1956)

    MathSciNet  MATH  Google Scholar 

  7. Iwasawa, K.: On the μ-invariants of ℤ l -extensions. In: Number Theory, Algebraic Geometry, and Commutative Algebra, in Honor of Yasuo Akizuki, pp. 1–11. Kinokuniya, Tokyo (1973)

    Google Scholar 

  8. Janusz, G.J.: Algebraic Number Fields, 2nd edn. Graduate Studies in Mathematics, vol. 7. American Mathematical Society, Providence (1996)

    MATH  Google Scholar 

  9. Ledet, A.: Brauer Type Embedding Problems. Fields Institute Monographs, vol. 21. American Mathematical Society, Providence (2005)

    MATH  Google Scholar 

  10. Neukirch, J.: Über das Einbettungsproblem der algebraischen Zahlentheorie. Invent. Math. 21, 59–116 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  11. Scholz, A., Taussky, O.: Die Hauptideale der kubischen Klassenkörper imaginär-quadratischer Zahlkörper: ihre rechnerische Bestimmung und ihr Einflußauf den Klassenkörperturm. J. Reine Angew. Math. 171, 19–41 (1934)

    Google Scholar 

  12. Tate, J.: Global class field theory. In: Algebraic Number Theory, Proc. Instructional Conf., Brighton, 1965, pp. 162–203. Thompson, Washington (1967)

    Google Scholar 

  13. Yahagi, O.: Construction of Number fields with prescribed l-class groups. Tokyo J. Math. 1, 275–283 (1978)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Manabu Ozaki.

Additional information

This research is partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 21540030, 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ozaki, M. Construction of maximal unramified p-extensions with prescribed Galois groups. Invent. math. 183, 649–680 (2011). https://doi.org/10.1007/s00222-010-0289-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00222-010-0289-0

Mathematics Subject Classification (2010)

Navigation